the geometry of the sphere
Cambridge.University.Press.The.Works.of.Archimedes.Volume.1.The.Two.Books.On.the.Sphere.and.the.Cylinder.Translation.and.Commentary.May.2004.pdf
Ngày tải lên :
21/09/2012, 11:00
... directly from the shape of the sphere It is typical that the center of the sphere is always an important point in the figures, and that the defining property of the equidistance of points on the surface ... when a cone cuts a sphere, having a vertex at the center of the sphere, I call the figure internally contained by the surface of the cone, and by the surface of the sphere inside the cone, a “solid ... the line drawn from the vertex of the segment to the circumference of the circle which is the base of the segment.5 Next to these, that, in every sphere, the cylinder having a The later reference...
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Tài liệu Đề tài " Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12, . . . " pptx
Ngày tải lên :
14/02/2014, 17:20
... be the union of Fn−1 with the loop-erasure of Xn Then F := ∞ Fn has the distribution of the n=1 (wired) USF on G The edges in F inherit the orientation from the loop-erased walks creating them, ... further condition on the occurrence of S, then we should also contract the edges in K1 and delete the edges in K2 Therefore, conditionally on ΥR and the occurrence of S, the path γR has the ... be the (set of edges of the) UST in G Then T , conditioned on T ∩ (E1 ∪ E2 ) = E1 (assuming this 483 GEOMETRY OF THE UNIFORM SPANNING FOREST event has positive probability), is the union of E1...
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geometry of the diric theory
Ngày tải lên :
27/03/2014, 11:52
... The Dirac algebra is the matrix algebra over the field of the complex numbers generated by the Dirac matrices We shall see that the conventional formulation of the Dirac equation in terms of the ... completely describes the effect of scattering, irrespective of the initial spin or polarization state The Real Dirac Theory To find a representation of the Dirac theory in terms of the STA, we begin ... interpretation of every feature of the free particle wave function It relates the mass to the spin to the phase of the wave function The phase simply describes the angle through which the electron...
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the differential geometry of parametric primitives
Ngày tải lên :
27/03/2014, 11:53
... to yield a sphere of arbitrary radius, we find that the expressions for the Jacobian, the Hessian, and the metric matrix remain the same, because x, y, and z scale linearly with r The curvature ... ∂ v∂u The normal curvature is defined to be positive a curve u on the surface turns toward the positive direction of the surface normal by: ˙ ˙ uDut κn = ˙ ˙t uG u The deviation (in the normal ... Differential Geometry of Parametric Primitives 26 January 1990 Reparametrization If the parametrization of the surface is transformed by the equations: u′ = u′(u,v) and v′ = v′( u,v) then the chain rule...
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mirrors and reflections- the geometry of finite reflection groups - a. borovik, a. borovik
Ngày tải lên :
31/03/2014, 16:16
... and thus made the exposition of the theory entirely geometrical The book contains a lot of exercises of different level of difficulty Some of them may look irrelevant to the subject of the book and ... the set of vertices of ∆ but is intransitive on the set of faces; Sym ∆ acts transitively on the set of faces of ∆ but is intransitive on the set of vertices; Sym ∆ is transitive on the set of ... t The group of symmetries of the regular n-gon ∆ is generated by two reflections s and t in the mirrors passing through the midpoint and a vertex of a side of ∆ Figure 2.7: For the proof of Theorem...
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the geometry of hamilton and lagrange spaces - miron, hrimiuc, shimara, sabau.
Ngày tải lên :
31/03/2014, 16:17
... using the Legendre transformation It defines a splitting of the tangent space of the cotangent bundle which is crucial for the description of the geometry of T*M The case when H is the square of ... motivation of the Lagrange geometry for higher order Lagrangians to the bundle of acclerations of order k, (or the osculator bundle of order k) denoted by and also the L-dual of this theory These ... vanish on the manifold It is called the Liouville vector field The existence of the Liouville vector field is very important in the study of the geometry of the manifold TM Let us consider the –linear...
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the geometry of schemes - eisenbud d., j.harris.
Ngày tải lên :
31/03/2014, 16:17
... is the (Krull) dimension of the local ring OX,x — that is, the supremum of lengths of chains of prime ideals in OX,x (The length of a chain is the number of strict inclusions.) The dimension of ... generalization of the idea of preimage of a set under a function in the notion of the fibered product of schemes To prepare for the definition, we first recall the situation in the category of sets The fibered ... (b) and (c) of Exercise I-46, the set of points of the fibered product of schemes X ×S Y is usually not equal to the fibered product (in the category of sets) of the sets of points of X and Y ...
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Introduction to the Geometry of the Triangle
Ngày tải lên :
05/06/2014, 18:36
... P They form the pedal triangle of P The pedal triangle of the orthocenter H is called the orthic triangle of ABC The pedal X of the orthocenter H on the side BC is also the pedal of A on the ... called the Euler triangle The circumcenter of the midway triangle of P is the midpoint of OP In particular, the circumcenter of the Euler triangle is the midpoint of OH, which is the same as N The ... computation of the inradius r and the radius of one of the tritangent circles of the triangle Consider the excircle Ia (ra ) whose center is the intersection of the bisector of angle A and the external...
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the mit press conceptual spaces the geometry of thought mar 2000
Ngày tải lên :
11/06/2014, 12:58
... by the programmed goals of the robot, these variables can then be transformed into a number of physical output magnitudes, for example, as the voltages of the motors controlling the left and the ... constituted of a number of higher harmonics The timbre of a tone, which is a phenomenal dimension, is determined by the relative strength of the higher harmonics of the fundamental frequency of the tone ... matched The hue of a color is related to the wavelengths of light, which thus is the main dimension used in the scientific description of color Visible light occurs in the range of 420-700nm The...
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Báo cáo hóa học: " Controlled Growth of Carbon Spheres Through the Mg-Reduction Route" pdf
Ngày tải lên :
22/06/2014, 00:20
... clear, and the shell thickness is about 50 nm The strong contrast between the dark edge and pale center is further the proof of its hollow nature [19] The yield of the carbon hollow spheres is ... needs to be increased further for the formation of solid carbon spheres The details of the process for the formation of carbon hollow spheres, hollow capsules and solid spheres are still not very ... that the sample prepared at 600 °C mainly consists of carbon solid spheres, which are round, smooth and clean The average diameter of the carbon solid spheres is about 250 nm The yield of the...
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Báo cáo toán học: "Tilings of the sphere with right triangles I: The asymptotically right families" ppsx
Ngày tải lên :
07/08/2014, 13:21
... gather together some elementary definitions and basic results used later in the paper We will represent the measure of the larger of the two non-right angles of the triangle by β and that of the ... in the union of the edges will be called an extended edge Each side of an extended edge is covered by a sequence of triangle edges; the sum of the edges on one side is equal to that on the other ... know whether there are other tilings with these triangles, as there are when n is even Despite the existence of two vertex vectors not used in any of the known tilings, we conjecture that there...
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Báo cáo toán học: "Tilings of the sphere with right triangles II: The (1, 3, 2), (0, 2, n) subfamily" ppt
Ngày tải lên :
07/08/2014, 13:21
... Proposition If the configuration of Figure 4b appears in a tiling of the sphere with the triangle T6 , centered on the (0, 5, 1) vertex O, then the tiling contains another copy of the same configuration ... 4), and (4, 0, 0) Its area is 1/80 that of the sphere Theorem The triangle T8 does not tile the sphere Proof: As before, we examine the properties of a hypothetical tiling and eventually reach a ... edges Proposition If the configuration of Figure 8c appears in a tiling of the sphere with the triangle T6 , the medium edge of triangle cannot be matched the electronic journal of combinatorics 13...
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Báo cáo toán học: "Tilings of the sphere with right triangles III: the asymptotically obtuse families" ppsx
Ngày tải lên :
07/08/2014, 15:22
... When d = the inequalities (3) are never satisfied When d = they are satisfied only for e = or 6, and in neither case does the area of the triangle divide that of the sphere Proposition The only ... vectors yielding the (90◦ , 90◦ , 90◦ ) triangle When d = they are satisfied for ≤ e < 12; but the only e for which the area of the triangle divides that of the sphere is 4, yielding the (90◦ , 90◦ ... continue the program of classifying the triangles that tile the sphere A more complete description of the program is given in [4] An important and still open problem involving monohedral tilings of the...
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Báo cáo toán học: "Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles - II" pptx
Ngày tải lên :
07/08/2014, 21:20
... j ≥ 2, the location of tile j can be deduced from the configuration of tiles (1, 2, , j − 1) and from the hypothesis that the configuration is part of a complete planar representation of a f-tiling ... representation The other choice on the sides of tile forces the configuration below (Figure 17) Tile of Figure 17 is forced in order to avoid the same situation of incompatibility as the one shown ... are ruled by the equation α + β = π, the vertices of valency surrounded by the angular sequence (α, α, α, α, γ, γ), and the vertices of valency 2p whose alternate sums are pδ = π The parameter...
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Báo cáo toán học: "Dihedral f-Tilings of the Sphere by Equilateral and Scalene Triangles - III" potx
Ngày tải lên :
07/08/2014, 21:21
... presence of a tile j as shown can be deduced from the configuration of tiles (1, 2, , j − 1) and from the hypothesis that the configuration is part of a complete local configuration of a f-tiling ... or β + γ + λ the electronic journal of combinatorics 15 (2008), #R147 10 In the first case, the other sum of angles would satisfy 2γ = π, which is impossible and in the second case the angle folding ... 118.57◦ The other sum of alternate angles at vertices surrounded by angles α, δ and γ is always (independently of the position of the kδ s) α + kδ + γ = π or β + (k + 1)δ = π Taking into account the...
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báo cáo khoa học: " The development and geometry of shape change in Arabidopsis thaliana cotyledon pavement cells" doc
Ngày tải lên :
11/08/2014, 11:21
... a correlation between the location of AMBs and the presence of dense pads of cellulose microfibrils at the interface of the anticlinal and outer periclinal (parallel to the leaf surface) cell ... uniform diffuse growth of the ribbon of anticlinal wall within the plane of the leaf Height increases in the anticlinal wall are unpredictable Page of 13 (Figure 5) and the behavior of this cell surface ... (Figure 2) and their presumed involvement in the synthesis of parallel arrays of cellulose microfibrils that would resist radial expansion of the cell perpendicular to the microfibril network...
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Báo cáo y học: " The fractal geometry of nutrient exchange surfaces does not provide an explanation for 3/4-power metabolic scaling" pdf
Ngày tải lên :
13/08/2014, 23:20
... the following, the theory of WBE is evaluated by first using a model of a 3-dimensional fractal-like network Then the rigor of the arguments used in deriving the results of the theory is evaluated ... the volume of a right cylinder is equal to the area of its circular cross section multiplied by the length of the cylinder The volume is not equal to the exterior surface area of the cyl- a b ... surface Their "maximum fracticality" is the dimension 3, which corresponds to a spacefilling surface The measure of the exchange surface area is the volume of the space within V that is filled by the...
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ON CONFIGURATIONS OF POINTS ON THE SPHERE AND APPLICATIONS TO APPROXIMATION OF HOLOMORPHIC FUNCTIONS BY LAGRANGE INTERPOLANTS
Ngày tải lên :
14/10/2015, 08:04
... ball) of center z ∈ CN and radius R > Let A be a nonempty set Let An denote the class of subsets of A containing n elements C ONFIGURATIONS OF POINTS ON THE SPHERE 2.1 Distance on the sphere ... (2.4) N −1 On the other hand, if Vd is not N-independent, then we set hVd = By definition, hVd is independent of the ordering of the vectors in Vd In the result below, we fix an order of Vd and ... hUd = diamd (Γ) (2.12) 2 The reverse inequality is a consequence of (1) Note that the proof of (2) also gives the following relation that we will use in the proof of (3), d−1 | sin ∏ j=0, j=k...
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